The image of someone running the gauntlet has always struck me as appropriate to much of math education.
You know the image, two rows of people with sticks, and you’re supposed to walk between them. As they hit you, you keep walking, until you fall. And they keep hitting.

I’ve talked to many people whose experience of their own math education is very much like running a gauntlet. At some stage, they fell and didn’t get back up. For them, math was essentially done, it was over, and they were defeated by it. For the rest of their lives, they relate to themselves as failures with respect to mathematics, as failures of the school system, or the school system as failing them.

This applies to students at all levels. I’ve talked to people who felt defeated by math class because they never quite understood long division in the elementary grades. I’ve talked to one who felt defeated by partial differential equations in engineering graduate school. For all, the common thread was that they were done with math and math was done with them.

Note that the decisive feature of the math gauntlet isn’t that they fell down, but that they felt they couldn’t get back up. It was over.

This experience is very different from that in history class, for instance. If Jesse fails his exam on the Civil War, he’s not likely to conclude that he’s now of course going to fail the exam on the Second World War. They appear as largely independent. Different dates to keep straight, different generals.

The thing that makes math class appear so unforgiving, so forbidable, is something that has less to do with math and more to do with the way that math class has historically evolved to the shape it has now. That is worth a closer look later.